A stochastic generalized Nash equilibrium model for platforms competition in the ride-hail market

The inherent uncertainties in the ride-hailing market complicate the pricing strategies of on-demand platforms that compete each other to offer a mobility service while striving to maximize their profit. Looking at this problem as a stochastic generalized Nash equilibrium problem (SGNEP), we design a distributed, stochastic equilibrium seeking algorithm with Tikhonov regularization to find an optimal pricing strategy. The proposed iterative scheme does not require a potentially infinite number of samples of the random variable to perform the stochastic approximation, thus making it appealing from a practical perspective. Moreover, we show that the algorithm returns a Nash equilibrium under mere monotonicity assumptions and a careful choice of the step size sequence, obtained by exploiting the specific structure of the SGNEP at hand.